Phase stability of a standing-wave free-electron laser

1407_68The standing-wave free-electron laser (FEL) differs from a conventional linear-wiggler microwave FEL in using irises along the wiggler to form a series of standing-wave cavities and in reaccelerating the beam between cavities to maintain the average energy. The device has been proposed for use in a two-beam accelerator because microwave power can be extracted more effectively than from a traveling-wave FEL. A simplified numerical simulation indicates that, with appropriate prebunching, the standing-wave FEL can produce an output signal that is effectively the same in all cavities. However, changes in the beam energy of less than 1% are found to introduce unacceptably large fluctuations of signal phase along the device. Analytic calculations and single-particle simulations are used here to show that the phase fluctuations result from beam synchrotron motion in the initial signal field, and an approximate analytic expression for the signal phase is derived. Numerical simulations are used to illustrate the dependence of phase fluctuations on the beam prebunching, the beam-current axial profile, and the initial signal amplitude